Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON3):

Solution:
def funky(n):
	arr = [(i*(i+1))/2 for i in range(1, 2*int(n**0.5) + 1)]
	i = 0
	j = len(arr)-1
	while i <= j:
		s = arr[i] + arr[j]
		if s == n:
			return True
		elif s < n:
			i+= 1
		else:
			j -= 1
	return False

n = int(input())
ans = funky(n)
print("YES" if ans else "NO")